A247671 Decimal expansion of Sum_{n >= 1} coth(Pi*n)/n^7 = (19/56700)*Pi^7.

1, 0, 1, 2, 0, 9, 1, 2, 0, 5, 0, 7, 5, 1, 1, 5, 5, 0, 7, 6, 3, 2, 6, 2, 6, 5, 1, 4, 4, 3, 3, 3, 1, 2, 0, 7, 7, 7, 1, 4, 8, 3, 6, 2, 7, 9, 1, 9, 9, 5, 1, 7, 5, 1, 3, 0, 9, 2, 2, 4, 7, 8, 8, 9, 8, 6, 3, 8, 3, 7, 0, 1, 3, 7, 3, 1, 5, 4, 5, 4, 2, 7, 4, 7, 4, 9, 6, 6, 4, 8, 7, 4, 5, 5, 2, 0, 6, 0, 8, 4

Offset

1,4

Comments

This identity was discovered by Ramanujan.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) p. 34.

Formula

Sum_{n >= 1} coth(Pi*n)/n^7 = (19/56700)*Pi^7.

Example

1.012091205075115507632626514433312077714836279199517513...

Mathematica

RealDigits[(19/56700)*Pi^7, 10, 100] // First

Prog

(PARI) default(realprecision, 100); (19/56700)*Pi^7 \\ G. C. Greubel, Aug 31 2018
(Magma) R:= RealField(100); (19/56700)*Pi(R)^7; // G. C. Greubel, Aug 31 2018

Crossrefs

Cf. A084258.

Sequence in context: A362952 A237289 A238396 * A011125 A345364 A197583

Adjacent sequences: A247668 A247669 A247670 * A247672 A247673 A247674

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 22 2014

Status

approved